AI 中文总结
本文为阿贝尔型 Shimura 簇的 Newton 层构造了 Frobenius--Hecke 对应的稳定迹公式，并给出内窥群贡献的群论判据，在酉情形展示了无内窥贡献的中间层。
AI 中文摘要
设 $(G,X)$ 是一个满足主定理假设的阿贝尔型 Shimura 数据，并假设相关的 Shimura 簇在 $p$ 处具有超特殊好约化。其特殊纤维由 $\sigma$-共轭类 $b\in B(G_{\mathbb{Q}_p},\mu_h^{-1})$ 分层。对于单个 Newton 层，本文构造了其紧支撑 $\ell$-adic 上同调上 Frobenius--Hecke 对应的交错迹的稳定化公式，系数取 $\ell$-adic 局部系统。该公式通过修改 Langlands--Kottwitz 方法获得，将这些 Lefschetz 数表示为 $G$ 的内窥群上的椭圆稳定几何分布，从而将上同调迹置于适合与自守谱数据比较的形式。我们还给出了一个群论判据，确定哪些椭圆内窥群能对给定的 Newton 层有贡献。对于某些酉 Shimura 簇，我们展示了一个中间 Newton 层，尽管环境 Shimura 簇的上同调中存在非平凡的内窥贡献，但该层没有非平凡的内窥贡献。
英文摘要
Let $(G,X)$ be a Shimura datum of abelian type satisfying the hypotheses of the main theorem, and suppose that the associated Shimura varieties have hyperspecial good reduction at $p$. Their special fibres are stratified by the $σ$-conjugacy classes $b\in B(G_{\mathbb{Q}_p},μ_h^{-1})$. For an individual Newton stratum, this paper constructs a stabilized formula for the alternating traces of Frobenius--Hecke correspondences on its compactly supported $\ell$-adic cohomology, with coefficients in an $\ell$-adic local system. The formula, obtained by modifying the Langlands--Kottwitz method, expresses these Lefschetz numbers as elliptic stable geometric distributions on endoscopic groups of $G$, placing the cohomological traces in a form suitable for comparison with automorphic spectral data. We also give a group-theoretic criterion determining which elliptic endoscopic groups can contribute to a given Newton stratum. For certain unitary Shimura varieties, we exhibit an intermediate Newton stratum with no non-trivial endoscopic contribution, although there are non-trivial endoscopic contributions in the cohomology of the ambient Shimura variety.
Comments104 pages
